Generalizations of Opial-Type Inequalities in Several Independent Variables

In this paper, we consider Willett’s and Rozanova’s generalizations of Opial’s inequality and extend them to inequalities in several independent variables. Also, we present some new Opial-type inequalities in several independent variables.

Inequalities similar to Opial's inequality involving higher order derivatives

In this paper we establish some new inequalities similar to Opial's inequality involving functions and their higher order derivatives. The analysis used in the proofs is elementary and our results provide a new range of nequalities of this type.

Weighted Opial inequalities

This paper presents a class of very general weighted Opial type inequalities. The notivation comes from the monograph of Agarwal and Pang (Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Acad., Dordrecht 1995) and the work of Anastassiou and Pecaric (J. Math. Anal. Appl. 239 (1999), 402-418). Assuming only a very general inequality, we extend the latter paper in several directions. A new result generalizing the original Opial's inequality is obtained, and applications to fractional derivatives are given.

A NOTE ON AN INEQUALITY SIMILAR TO OPIAL'S INEQUALITY

In the present note we establish a new inequality similar to Opial's inequality by using a fairly elementary analysis.